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Algebraic Algorithms

100

Solve the equation for x:

3/(x+5) = 2(2x + 3)

x = 1/4 (or x = 0.25)

200

Solve the following expression, given that x = 1/2, y = -2/3 and z = 3/4

(1/x - 1/y - 1/z)²

169/36

300

simplify the expression by rationalizing the denominator:

(x sqrt 3)/ sqrt x

sqrt 3x

99 Problems but a word aint one.

100

Find the equation of the line parallel to x = 3 and contains the point (2, -5)

x = 2

200

$1000 is invested in a bank at 20% interest. How long will it take for the investment to triple?

10 years

300

Express 81/3^x as a power of 3 and solve for x if 81/3^x = 9.

3⁴/3^x = 3²      x = 2

Geometry Gems

100

Find the value of x given that angle 1 is complementary to angle 2. 

Angle 1 = 3x + 4       Angle 2 = 2x + 11

x = 15

200

Given that angle 1 and angle 2 are corresponding angles, find the value of x

angle 1 = 5x + 7        angle 2 = 4x + 30

x = 23

300

Given isosceles triangle with a base angle of 3x and a vertex angle of 30, find the value of x. 

x = 25

Conjunction Function

100

Given the function f(x) = 3x - 2, find the values of f(-1), f(0), and f(1)

f(-1) = -5, f(0) = -2, f(1) = 1

200

Given that f(x) = 3x + 7, when does f(x) = 10

x = 1

300

Find the value of x given the two points (x, 4) and (2, 2) have a slope of -2/3.

x = 1